What does the Hebrew phrase “Leshanah tovah tikatev v’tihatem” mean? How is it used?

It means literally, “May you be inscribed and sealed for a good year”, and is a blessing traditionally given by observant Jews to one another during the first ten days of the Jewish New Year. The idea is that during that time, God decides what your fate will be in the coming year, and inscribes it in the Book of Life (and seals it on Yom Kippur, the Day of Atonement, which falls ten days into the Jewish Year).